A statistical investigation of the mass discrepancy–acceleration relation

Abstract

We use the mass discrepancy-acceleration relation (the correlation between\nthe ratio of total-to-visible mass and acceleration in galaxies; MDAR) to test\nthe galaxy-halo connection. We analyse the MDAR using a set of 16 statistics\nthat quantify its four most important features: its shape, its scatter, the\npresence of a "characteristic acceleration scale," and the correlation of its\nresiduals with other galaxy properties. We construct an empirical framework for\nthe galaxy-halo connection in LCDM to generate predictions for these\nstatistics, starting with conventional correlations (halo abundance matching;\nAM) and introducing more where required. Comparing to the SPARC data, we find\nthat: 1) the approximate shape of the MDAR is readily reproduced by AM, and\nthere is no evidence that the acceleration at which dark matter becomes\nnegligible has less spread in the data than in AM mocks; 2) even under\nconservative assumptions, AM significantly overpredicts the scatter in the\nrelation and its normalisation at low acceleration, and furthermore positions\ndark matter too close to galaxies' centres on average; 3) the MDAR affords 2\nsigma evidence for an anticorrelation of galaxy size and Hubble type with halo\nmass or concentration at fixed stellar mass. Our analysis lays the groundwork\nfor a bottom-up determination of the galaxy-halo connection from relations such\nas the MDAR, provides concrete statistical tests for specific galaxy formation\nmodels, and brings into sharper focus the relative evidence accorded by galaxy\nkinematics to LCDM and modified gravity alternatives.\n